Abstract: Aiming at the problem of large steady-state error of dual-mode repetitive control in grid frequency fluctuations, an improved infinite impulse response（IIR） filter based on Thiran algorithm of cascaded structure is proposed. This improved IIR filter can effectively approximate the fractional delay link and improve the steady-state tracking accuracy of the system. In this paper, a cascade structure derived from the continued fraction is used to replace the direct structure of the previous implementation of the Thiran algorithm. Moreover, the designed cascade structure Thiran algorithm can be used in the IIR filter to adjust the filter parameters online, and compared with the previous direct structure, each block of the cascade structure can be implemented with two multipliers, which simplifies the parameter design and facilitates the application and promotion. Based on the fractional-order dual-mode repetitive controller（FO-DMRC）, and using the current control strategy of proportional and FO-DMRC combination, the inverter is controlled to output high-quality grid-connected current. Finally, simulation and experimental results verify the accuracy and effectiveness of the proposed strategy.